Abstract The planar Skorokhod embedding problem was first proposed and solved by Gross ‘A conformal Skorokhod embedding’, Electron. Commun. Probab. 24 (2019), 11 pages; doi: 10. 1214/19-ECP272. Gross worked with probability distributions having finite second moment. Boudabra and Markowsky ‘Remarks on Gross’ technique for obtaining a conformal Skorokhod embedding of planar Brownian motion’, Electron. Commun. Probab. 25 (2020), 13 pages; doi: 10. 1214/20-ECP300 extended the solution to all distributions with a finite p th moment for p>1. The case p=1 has remained uncovered since then. In this note, we show that the planar Skorokhod embedding problem is solvable for p=1 when the Hilbert transform of its quantile function is integrable, effectively closing this line of investigation.
Maher Boudabra (Thu,) studied this question.